Line of Intersection of Two Planes

In this video we look at a common exercise where we are asked to find the line of intersection of two planes in space. As long as the two planes are not parallel to each other, there will be a line of intersection. In this video we go through the algebra for how to find this line of intersection.

[Patrick_Knowlton]

I'm using this to find out how many each of three different crop seeds I should buy in Stardew it feels so strange using math like this in a casual scenario lol

[WaitinForAMate]

That is such a great technique to finding intersection lines between two planes. Thank you so much for your clear and easy to follow lesson :)

[kshitiz]

Nice technique Prof. I was trying to use the cross product of normals to find the direction ratios of the line of intersection. Although, I got stuck how to proceed from there, your little lecture helped me. Thanks, from India.

[Observe]

Your videos are flawless! you're a great asset to any 6th from student (me included :L) i only wish i found your videos sooner!! never stop making them man!! Big up yuhself 

[naderbelal]

I would like to thank you for this video ... it had helped me to solve a parametric geometrical problem

[harsh.ww]

you can also put z = 0, solve for y and x (faster method)

[jamie]

Best video on this topic.. Others were driving me crazy taking forever to explain it in convoluted ways. It could be found just by doing RREF on augmented matrix to find parametric form, and this explains that in terms that someone who had only done regular algebra before could conceptualize.

[leocadieploumen]

I have a question, why is y=y?, why is that obviously?

[TabooTalz]

Thank you so much, I've tried two other methods to learn this (including the one my text book and teacher recommend) and I've never understood this until now. It's worth 5 marks usually so I really needed this

[luisrodriguez-mxme]

can you also find the normal vectors, take the cross product, find a point of interception, then create a line out of the?

[priyanshukhandelwal]

We can find the cross product of these two plane vectors(normal vectors) and then just put x or y or z = 0 and then we will have two equations (planes) in terms of x and y..(if we put z=0) from there we can find value of x, y.... Hence we will have a point (x, y, 0) on line of intersection and a vector parallel to line of intersection... Now we can easily find line of intersection

[Nhalok]

Thank you Firefly. You have helped me love maths again. A priceless gift.
Thank you.

[aybarspektas]

That was crystal clear, thanks a lot!

[shahsingh]

Your lec is owsam .love❤ from india 🇮🇳

[MLGJuggernautgaming]

Great advice and help! I found it much easier though to just take the cross product of the two planes' normal vectors and get a point on the line. It advice all the system of equations and possible mistake that can be made along the way.

[gurra]

Another easy way to do it would be to get the vectors of the two planes, n1 and n2. And by them create an orthogonal vector through cross product. So n1 x n2 = v or whatever you wanna call the cross vector. Since it's a line we "add" the vector with the corresponding point of the line.

Side question, is it that important to get the point you got there or is it just adequate to get any arbitrary point on the line and then add the vector?

[Bembrand]

Great from Addis Ababa University, Ethiopia

[Dom-qocf]

thanks for the help! it was a good refresher

[yohannesbeneberu]

Find an equation for the plane that contains the line x=1+t, y=3t, z=2tand is parallel to the line of intersection of the planes –x+2y+z=0 and x+z=-1.

[wilveryescas]

i read the whole chapter in the calc book and could not understand this problem but now thanks to you i get it thanks